Number of energy levels

I have been told that as were go further away from the nucleus, the energy levels get closer and closer together - do we get to a stage where we get no more? I assume we must because any energy above this causes the substance to ionise (ie the ionisation energy); but are there an infinate number of energy levels before this or some discrete number of them?

I have been told that the way that the levels get closer and closer together is governed by some equation - what I guess I'm asking boils down to is is this an infinate geometric progression with the levels getting closer and closer for infinity (ie - an infinate number of levels), or do we get to a point where an equation would just give the same answer - there are no more levels which exist?

I have been told that as were go further away from the nucleus, the energy levels get closer and closer together

Yes,that's a physical consequence of Bohr's model/postulates.

Cheman said:

- do we get to a stage where we get no more?

I

As soon as u go past zero,yes,the electron is free,adieu to quantization.

Cheman said:

but are there an infinate number of energy levels before this

Sure,the discrete spectrum contains an infinite # of energy levels.

Cheman said:

I have been told that the way that the levels get closer and closer together is governed by some equation

Yes.This equation
[tex] E_{n}=\frac{E_{1}}{n^{2}} [/tex]

Cheman said:

- what I guess I'm asking boils down to is is this an infinate geometric progression with the levels getting closer and closer for infinity (ie - an infinate number of levels), or do we get to a point where an equation would just give the same answer - there are no more levels which exist?